Promoting sustainable soil management is a possible option for achieving net-zero greenhouse gas emissions in the future. Several efforts in this area exist, and the application of spatially explicit models to anticipate the effect of possible actions on soils at a regional scale is widespread. Currently, models can simulate the impacts of changes on land cover, land management, and the climate on the soil carbon stocks. However, existing modeling tools do not incorporate the lateral transport and deposition of soil material, carbon, and nutrients caused by soil erosion. The absence of these fluxes may lead to an oversimplified representation of the processes, which hinders, for example, a further understanding of how erosion has been affecting the soil carbon pools and nutrients through time. The sediment transport during deposition and the sediment loss to rivers create dependence among the simulation units, forming a cumulative effect through the territory. If, on the one hand, such a characteristic implies that calculations must be made for large geographic areas corresponding to hydrological units, on the other hand, it also can make models computationally expensive, given that erosion and redeposition processes must be modeled at high resolution and over long timescales. In this sense, the present work has a three-fold objective. First, we provide the development details to represent in matrix form a spatially explicit process-based model coupling sediment, carbon, and erosion, transport, and deposition (ETD) processes of soil material in hillslopes and valley bottoms (i.e., the CE-DYNAM model). Second, we illustrate how the model can be calibrated and validated for Europe, where high-resolution datasets of the factors affecting erosion are available. Third, we presented the results for a depositional site, which is highly affected by incoming lateral fluxes from upstream lands. Our results showed that the benefits brought by the matrix approach to CE-DYNAM enabled the before-precluded possibility of applying it on a continental scale. The calibration and validation procedures indicated (i) a close match between the erosion rates calculated and previous works in the literature at local and national scales, (ii) the physical consistency of the parameters obtained from the data, and (iii) the capacity of the model in predicting sediment discharge to rivers in locations observed and unobserved during its calibration (model efficiency (ME) =0.603, R2=0.666; and ME =0.152, R2=0.438, respectively). The prediction of the carbon dynamics on a depositional site illustrated the model's ability to simulate the nonlinear impact of ETD fluxes on the carbon cycle. We expect that our work advances ETD models' description and facilitates their reproduction and incorporation in land surface models such as ORCHIDEE. We also hope that the patterns obtained in this work can guide future ETD models at a European scale.